Thats kinda the whole point of the article, in fact. All possible encodings of all possible thoughts, books, formal systems, and whatever, fit into the rationals, and the reals are categorically outside that.
All books written and will be written (in finite time) - yes, rational.
All possible questions (infinitely many) - no, that would be a non-terminating non-periodic binary, right. From the article:
> 2.4 Borel’s know-it-all number
> The idea of being able to list or enumerate all possible texts in a language is an extremely powerful one, and it was exploited by Borel in 1927 [Tasi ́c, 2001, Borel, 1950] in order to define a real number that can answer every possible yes/no question!
> You simply write this real in binary, and use the nth bit of its binary expansion to answer the nth question in French.
> Borel speaks about this real number ironically. He insinuates that it’s illegitimate, unnatural, artificial, and that it’s an “unreal” real number, one that there is no reason to believe in.
